Best Known (17, s)-Sequences in Base 8
(17, 64)-Sequence over F8 — Constructive and digital
Digital (17, 64)-sequence over F8, using
- t-expansion [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
(17, 135)-Sequence in Base 8 — Upper bound on s
There is no (17, 136)-sequence in base 8, because
- net from sequence [i] would yield (17, m, 137)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (17, 121, 137)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8121, 137, S8, 104), but
- the linear programming bound shows that M ≥ 13066 856935 963523 721024 625401 270709 435452 350217 785478 549632 311553 515794 037630 134130 713931 717708 202057 690742 978515 268863 524864 / 568 730779 782165 > 8121 [i]
- extracting embedded orthogonal array [i] would yield OA(8121, 137, S8, 104), but
- m-reduction [i] would yield (17, 121, 137)-net in base 8, but